Question

If AB has endpoint A(2, 13) and midpoint
(10,-1) then give the coordinate of B.

Answer 1

Given: Line coordinates P(10,-1) A-------------------------------------------B (2,13) (x, y)
The point P(x', y') divides AB in 1:1 ratio =m:n
So from formula:
x' =(mx1 + nx2)/(m+n) and y' = (my1+ny2)/(m+n) where (x',y')=(10,-1), m:n=1:1 and (x1, y1)=(2,13), (x2,y2)=(x,y)
Put the values in the formula: 10 = 1(2)+1(x)/1+1 = (2+x)/2 =>20=2+x from cross multiplication =>x=20-2=18 from transposition =>x=18 -1=1(13)+1(y)/1+1 =(13+y)/2 =>-2=13+y from cross multiplication =>y=-2-13=-15 from transposition =>y=-15 So coordinates of B (18,-15)

Answer 2

(18, -15)

Explanation:

The vector AB is defined by its starting and endpoints. Usually, B would be at the end, but in this case A is. Since we are given its midpoint, that is, the point equidistant from both the coordinates A and B, we can find coordinate B by simply calculating the distance between A and the midpoint and reapplying this distance to the midpoint.

1. Finding the distance between the midpoint and A:

The distance between two coordinates, from what I can recall, is simply the final coordinate value minus the initial coordinate value, following the form (x2-x1, y2-y1). We know that A comes after the midpoint, because it is the endpoint (so it will be the final coordinate value). Applying this to the context of the question, (2-10, 13+1) = (-8,14).

2. Finding B using the distance between midpoint and A:

B will be the initial coordinate value because it comes before the midpoint. Therefore, giving B the values (x,y): (10-x, -1-y) = (-8, 14). Separating into two equations (respective to each axis):

10-x=-8

-x=-18

x=18

-1-y=14

-y=15

y=-15

Therefore, the coordinate of B is (18, -15).